Bethe-Salpeter equation forI=1nucleon-nucleon scattering with one-boson exchange

Abstract

We extend our earlier work on the Bethe-Salpeter equation for $J=0\mathrm{}$ by considering in addition the isospin $I=1\mathrm{}$ phase shifts ${}_{}{}^3{}_{}{}^{}P_1^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}P_2^{}{}_{}{}^{}$, ${}_{}{}^3{}_{}{}^{}F_2^{}{}_{}{}^{}$, ${\epsilon }_2$, and ${}_{}{}^1{}_{}{}^{}D_2^{}{}_{}{}^{}$. These require the solution of a system of eight (instead of four for $J=0\mathrm{}$) coupled integral equations which have again been solved by iteration and application of the Padé method. The kernel is the same as before; i.e., the same particles are exchanged with the same analytic form of the cutoff. However, in order to find a fair agreement of our phase shifts with the experimental data, it was necessary to lower the cutoff mass. The phase shifts obtained show the general deficiency of dropping too fast at higher energies. In addition, we have studied the operator Padé approach and find that relatively few off-shell states are indeed sufficient to obtain reasonable accuracy for the summation of the Born series in a one-loop approximation.